A method for solving the wave aberration of an optical system by ray tracing

Abstract

A method for solving the wave aberration of an optical system by ray tracing, belonging to the technical field of optical design, includes: Step 1, determining the relevant parameters of a virtual reference spherical surface; Step 2, calculating the optical path that the light beam emitted from the object point travels from the object point to the virtual reference spherical surface; Step 3, calculating the optical path that the chief ray travels from the object point to the exit pupil plane; Step 4, solving the wave aberration of the optical system by using the optical paths obtained in Step 2 and Step 3. The method for solving the wave aberration of an optical system by ray tracing of the present invention provides a relatively simple solution method for the detection and measurement of the wave aberration of an optical system. Compared with the existing detection devices or detection systems, it has the advantages of simple calculation and small amount of calculation, and at the same time reduces the research and design costs of subsequent optical design software.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical design, and particularly relates to a method for solving the wave aberration of an optical system by ray tracing. Background Art

[0002] Wave aberration is one of the most fundamental and crucial indicators for evaluating the imaging quality of an optical system, and it is also a bridge connecting geometric optics and wave optics. How to calculate the wave aberration of an optical system is a basic and key issue in the process of developing optical design software. Wave aberration is generally defined as the optical path difference between the actual wavefront and the reference wavefront (also called the reference spherical surface or ideal wavefront) of an optical system. However, only relying on the definition, it is impossible to know how to calculate the wave aberration of an optical system.

[0003] Currently, the detection or measurement of the wave aberration of an optical system is mostly achieved by using a detection device or a detection system. For example, in the Chinese patent "A Wave Aberration Detection System and Measurement Method" with the publication number CN109855842A, this patent uses a spherical wave to irradiate a wave aberration measurement device and a projection objective lens, measures the first wavefront information (without installing the projection objective lens) and the second wavefront information by using the spherical wave to irradiate the wave aberration measurement device, and obtains the final wave aberration information based on the first wavefront information and the second wavefront information. Another example is the Chinese patent "A Wave Aberration Measurement Device" with the publication number CN104111161A, which includes a light source, an illumination system, an object plane mask, a projection objective lens, and an image plane detection unit. The illumination beam formed after passing through the light source and the illumination system is incident on the object plane mask on the object plane of the projection objective lens to form an ideal spherical wave; the spherical wave carrying the wave aberration of the projection objective lens is detected by the image plane detection unit to obtain the wave aberration information of the projection objective lens.

[0004] Most of the existing detection or measurement methods for the wave aberration of an optical system use a detection device or a detection system composed of relatively complex structures. These detection devices or detection systems composed of complex structures increase the R & D cost of optical design software and are not conducive to the research and design of optical design software. Currently, there is no reported method for solving the wave aberration of an optical system by ray tracing. Summary of the Invention

[0005] In order to solve the problems existing in the prior art, the present invention provides a method for solving the wave aberration of an optical system by ray tracing. The present invention can solve the wave aberration of an optical system on the premise of tracing the propagation path of light rays in the optical system.

[0006] The technical solution adopted by the present invention to solve the technical problems is as follows:

[0007] A method for solving the wave aberration of an optical system by ray tracing according to the present invention includes the following steps:

[0008] Step 1: Determine the relevant parameters of the virtual reference sphere;

[0009] Step 2: Calculate the optical path that the light beam emitted from the object point travels from the object point to the virtual reference sphere;

[0010] Step 3: Calculate the optical path that the chief ray travels from the object point to the exit pupil plane;

[0011] Step 4: Solve for the wave aberration of the optical system using the optical paths obtained in Step 2 and Step 3.

[0012] Furthermore, the wave aberration of the optical system is the optical path difference between the actual wavefront and the reference wavefront of the optical system. The reference wavefront is a spherical surface, which is defined as the virtual reference sphere. The center of the virtual reference sphere is located at the position of the Gaussian image point, and the radius of curvature of the virtual reference sphere is the distance between the exit pupil center and the Gaussian image point.

[0013] Furthermore, the specific operation steps of Step 1 are as follows:

[0014] Step S1.1: Using Gaussian optical imaging theory, based on the object point position and the composition of the optical system components, successively image the object point using each optical component in the optical system, and calculate the position of the Gaussian image point formed by the object point after passing through the optical system. This Gaussian image point is the center of the virtual reference sphere;

[0015] Step S1.2: According to the position parameters of the aperture stop of the optical system and the composition of the optical system components, calculate the position of the exit pupil of the optical system, and calculate the distance between the exit pupil center and the Gaussian image point. This distance is equal to the radius of curvature of the virtual reference sphere.

[0016] Furthermore, the specific operation steps of Step 2 are as follows:

[0017] Step S2.1: According to the position parameters of the aperture stop of the optical system and the composition of the optical system components, calculate the position and aperture size of the entrance pupil of the optical system;

[0018] Step S2.2: Set a grid with a certain resolution on the entrance pupil plane of the optical system, include the entrance pupil within these grids, and determine the positions of all grid points on the entrance pupil plane; for each grid point, determine the parameters of a traced incident ray, that is, the traced incident ray passes through the object point, and the incident direction of the traced incident ray is along the line connecting the object point and the grid point; traverse all grid points on the entrance pupil plane and determine the parameters of all traced incident rays in the same way;

[0019] Step S2.3: Determine the paths that all traced incident rays travel from the object point to the virtual reference sphere;

[0020] Step S2.4: Calculate the optical paths that all traced incident rays travel from the object point to the virtual reference sphere.

[0021] Further, in step S2.2, the resolution of the grid is 64*64 or 128*128.

[0022] Further, the specific operation steps of step S2.3 are as follows:

[0023] Trace the propagation path of each incident ray among all the traced incident rays. The propagation path includes the normal propagation path and the reverse extension line propagation path. If the virtual reference spherical surface is on the ray propagation path, it is the normal propagation path. At this time, calculate the intersection point between the incident ray and the virtual reference spherical surface. If the virtual reference spherical surface is in the direction opposite to the ray propagation direction, it is the reverse extension line propagation path. At this time, calculate the intersection point between the reverse extension line of the incident ray and the virtual reference spherical surface.

[0024] Further, the specific operation steps of step S2.4 are as follows:

[0025] For each incident ray among all the traced incident rays, first calculate the optical path that it travels from the object point to the last optical element of the optical system according to its propagation path in the optical system, and then calculate the optical path that the incident ray travels from the last optical element of the optical system to the virtual reference spherical surface according to the exit point and the exit direction of the incident ray on the last optical element of the optical system.

[0026] Further, in step S2.4, use a two-dimensional matrix Ψ1 to represent the optical path that the light beam emitted from the object point travels from the object point to the virtual reference spherical surface:

[0027]

[0028] Among them, a(x i , y j ) represents the optical path that the incident ray with the normalized coordinates (x i , y j ) travels from the object point to the virtual reference spherical surface. i = 1…m, j = 1…n, and the size of the two-dimensional matrix Ψ1 is m×n.

[0029] Further, the specific operation steps of step three are as follows:

[0030] Assume that the optical path that the chief ray travels from the object point to the exit pupil surface is b. Define a two-dimensional matrix Ψ2 with the same size as the two-dimensional matrix Ψ1, and all its elements are b. The two-dimensional matrix Ψ2 represents the optical path that the light beam emitted from the object point travels through the optical system to the actual wave surface.

[0031]

[0032] Further, the specific operation steps of step four are as follows:

[0033] Define a two-dimensional matrix Δ that describes the wave aberration data of an optical system. The size of the two-dimensional matrix Δ is m×n. The calculation formula for the two-dimensional matrix Δ is Formula (3) or Formula (4).

[0034] Δ = Ψ1 - Ψ2 (3)

[0035] Δ = Ψ2 - Ψ1 (4)

[0036] The basic principle on which the present invention is based is as follows:

[0037] (1) Wave aberration is defined as the optical path difference between the actual wavefront and the reference wavefront. Here, both the "actual wavefront" and the "reference wavefront" refer to the position at the exit pupil, and the actual wavefront and the reference wavefront intersect at the center of the pupil.

[0038] (2) Solving the "actual wavefront" is relatively complex in the actual process. The optical path from the object point to the reference wavefront can be directly calculated, which includes the optical path of the light beam emitted from the object point to the "actual wavefront" and the optical path difference between the "actual wavefront" and the "reference wavefront".

[0039] (3) The optical paths of different light rays in the light beam emitted from the object point to the "actual wavefront" are the same because the "actual wavefront" is an "equiphase surface", that is, an "equal optical path surface".

[0040] (4) The "actual wavefront" and the "reference wavefront" intersect at the center of the exit pupil. Therefore, the optical path from the light ray emitted from the object point to the "actual wavefront" is equal to the optical path that the chief ray emitted from the object point travels to the exit pupil plane (intersecting at the center of the exit pupil).

[0041] The beneficial effects of the present invention are:

[0042] A method for solving the wave aberration of an optical system by ray tracing according to the present invention provides a relatively simple solution method for the detection and measurement of the wave aberration of an optical system. Compared with the existing detection devices or detection systems, it has the advantages of simple calculation and small amount of calculation, and at the same time reduces the research and design costs of subsequent optical design software. Brief Description of the Drawings

[0043] Figure 1 It is a flowchart of a method for solving the wave aberration of an optical system by ray tracing according to the present invention. Detailed Embodiments

[0044] The following further describes the present invention in detail with reference to the accompanying drawings.

[0045] As Figure 1As shown in the figure, a method for solving the wave aberration of an optical system by ray tracing according to the present invention calculates the wave aberration at specific field of view and specific aperture coordinates of the optical system through ray tracing (i.e., tracing the ray path), and specifically includes the following steps:

[0046] Step 1: Determine the relevant parameters of the virtual reference sphere, including the position of the sphere center, the radius of curvature, etc.

[0047] The wave aberration is defined as the optical path difference between the actual wavefront and the reference wavefront of the optical system. Among them, the reference wavefront is a spherical surface, the center of the sphere is located at the position of the Gaussian image point, and the radius of curvature is the distance between the center of the exit pupil and the Gaussian image point. Specifically, the position of the reference wavefront can be determined according to the following operation steps.

[0048] Step S1.1: Calculate the position of the Gaussian image point formed after the object point passes through the optical system. This Gaussian image point is the center of the reference sphere. Specifically:

[0049] Using the Gaussian optical imaging theory, according to the position of the object point and the composition of the optical system components, the object point is imaged by each optical component in the optical system in turn, and finally the position of the Gaussian image point is obtained.

[0050] Step S1.2: Calculate the position of the exit pupil of the optical system, and then calculate the radius of curvature of the reference sphere.

[0051] According to the position parameters of the aperture stop of the optical system and the composition of the optical system components, calculate the position of the exit pupil of the optical system. On this basis, calculate the distance between the center of the exit pupil and the Gaussian image point, and this distance is equal to the radius of curvature of the reference sphere.

[0052] This reference sphere is not an actually existing optical surface, but the position of the intersection of the ray and this reference sphere needs to be calculated in the subsequent steps. Therefore, this reference sphere is called a virtual reference sphere in the following.

[0053] Step 2: Calculate the optical path that the light beam (ray array) emitted from the object point travels from the object point to the virtual reference sphere.

[0054] Since both the actual wavefront and the reference wavefront of the optical system are two-dimensional concepts, the wave aberration (i.e., the optical path difference between the actual wavefront and the reference wavefront of the optical system) is generally also a two-dimensional concept. To describe the two-dimensional wave aberration distribution, a series of rays emitted from the object point and evenly distributed at the intersection with the pupil plane need to be traced. Finally, the calculation result of the wave aberration is also a two-dimensional matrix, which is used to describe the discrete wave aberration distribution data. If high-resolution wave aberration distribution data is to be obtained, when performing ray tracing on the light beam emitted from the object point, the number of incident rays to be traced needs to be increased, that is, the sampling density of the incident rays to be traced is increased.

[0055] The specific operation steps are as follows:

[0056] Step S2.1: Calculate the position and aperture size of the entrance pupil of the optical system.

[0057] Based on the position parameters of the aperture stop of the optical system and the composition of the optical system components, calculate the position and aperture size of the entrance pupil of the optical system. When calculating, existing calculation methods can be used with reference to engineering optics textbooks.

[0058] Step S2.2: Determine the parameters of the incident ray to be traced (ray array).

[0059] Set a grid with a certain resolution on the entrance pupil plane of the optical system, such as 64*64 or 128*128, etc., and include the entrance pupil in these grids to determine the positions of all grid points on the entrance pupil plane. For each grid point, the parameters of an incident ray to be traced can be determined, that is, the incident ray to be traced passes through the object point, and the incident direction of the incident ray to be traced is along the line connecting the object point and this grid point. Traverse all grid points on the entrance pupil plane, and in the same way, the parameters of all incident rays to be traced (ray array) can be finally determined.

[0060] Step S2.3: Determine the path that the incident ray to be traced (ray array) travels from the object point to the virtual reference sphere.

[0061] Trace the propagation path of each incident ray in the incident ray to be traced (ray array) until it "propagates" through the last optical element of the optical system to the position of the virtual reference sphere. Here, "propagation" has some special meanings, including normal propagation and reverse extension line propagation: if the virtual reference sphere is on the ray propagation path, it is normal propagation, and the intersection point between the incident ray and the virtual reference sphere is calculated; if the virtual reference sphere is in the direction opposite to the ray propagation direction, it is reverse extension line propagation, and the intersection point between the reverse extension line of the incident ray and the virtual reference sphere is calculated.

[0062] Step S2.4: Calculate the optical path that the incident ray to be traced (ray array) travels from the object point to the virtual reference sphere.

[0063] For each incident ray in the traced incident ray (ray array), first, according to its propagation path in the optical system, calculate the optical path it travels from the object point to the last optical element of the optical system; then, according to the exit point and exit direction of the incident ray on the last optical element of the optical system, calculate the optical path that the incident ray "travels" from the last optical element of the optical system to the virtual reference sphere. Here, "travels" includes normal propagation (the virtual reference sphere is on the ray propagation path) and reverse extension propagation (the virtual reference sphere is in the direction opposite to the ray propagation direction); if the incident ray propagates normally to the virtual reference sphere (normal propagation), then the sum of the former two optical paths (the sum of the optical path that the ray travels from the object point to the last optical element of the optical system and the optical path that the ray travels from the last optical element of the optical system to the virtual reference sphere) is the one sought; if the reverse extension of the incident ray intersects the virtual reference sphere (reverse extension propagation), then the result of subtracting the latter from the former (the difference between the optical path that the ray travels from the object point to the last optical element of the optical system and the optical path that the ray travels from the last optical element of the optical system in the reverse direction to the virtual reference sphere) is the one sought.

[0064] The specific operation steps are as follows:

[0065] Use the two-dimensional matrix Ψ1 to represent the optical path that the light beam (ray array) emitted from the object point travels from the object point to the virtual reference sphere. The two-dimensional matrix Ψ1 can be simply expressed as:

[0066]

[0067] where a(x i , y j ) represents the optical path that the incident ray with the normalized coordinates (x i , y j ) travels from the object point to the virtual reference sphere, and i = 1…m, j = 1…n.

[0068] Here, (x i , y j ) represents the normalized coordinates of the intersection point of the incident ray (or its reverse extension) and the pupil plane. This coordinate can be used in the subsequent process of polynomial fitting of the wave aberration (after solving the wave aberration of the optical system); m and n are used to describe the size of the wave aberration distribution data matrix, which characterizes the resolution of the wave aberration distribution data.

[0069] Step 3: Calculate the optical path that the chief ray travels from the object point to the exit pupil plane (intersecting at the exit pupil center).

[0070] Calculate the optical path that the chief ray emitted from the object point passes through the optical system and propagates to the center of the exit pupil. Since the actual wavefront of the optical system passes through the center of the exit pupil, this optical path can represent the optical path that the ray passes from the object point through the optical system to the actual wavefront. Similarly, it should still be noted here that the chief ray may not actually pass through the center of the exit pupil, but only the reverse extension line of the chief ray passes through the center of the exit pupil. In this case, the calculation of the optical path needs to be carried out in the manner described in Step 2.

[0071] Assume that the optical path that the chief ray passes from the object point to the exit pupil plane (intersecting at the center of the exit pupil) is b. Here, a two-dimensional matrix Ψ2 of the same size (m×n) as the two-dimensional matrix Ψ1 is defined, and all its elements are b. The two-dimensional matrix Ψ2 represents the optical path that the light beam (ray array) emitted from the object point passes through the optical system to the actual wavefront:

[0072]

[0073] Step 4: Calculate the wave aberration of the optical system by using the optical path of each ray in the light beam obtained in Step 2 and the optical path of the chief ray obtained in Step 3.

[0074] Define a two-dimensional matrix Δ that describes the wave aberration data of the optical system (the size of this two-dimensional matrix Δ is also m×n). The wave aberration is defined as the optical path difference between the actual wavefront and the reference wavefront of the optical system. Among them, the two-dimensional matrix Ψ1 represents the optical path that the light beam (ray array) emitted from the object point passes from the object point to the virtual reference spherical surface, and the two-dimensional matrix Ψ2 represents the optical path that the light beam (ray array) emitted from the object point passes through the optical system to the actual wavefront. Then the two-dimensional matrix Δ can be expressed as the difference between the two-dimensional matrix Ψ1 and the two-dimensional matrix Ψ2, that is:

[0075] Δ = Ψ1 - Ψ2 (3)

[0076] Or

[0077] Δ = Ψ2 - Ψ1 (4)

[0078] Which specific calculation method to adopt depends on the positive and negative sign criterion of the wave aberration data of the optical system.

[0079] The above description is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for solving the wave aberration of an optical system by ray tracing, characterized in that, Including the following steps: Step 1: Determine the relevant parameters of the virtual reference sphere; Step 2: Calculate the optical path that the light beam emitted from the object point travels from the object point to the virtual reference sphere; Step S2.1: Calculate the position and aperture size of the entrance pupil of the optical system according to the position parameters of the aperture stop of the optical system and the composition of the optical system components; Step S2.2: Set a grid with a certain resolution on the entrance pupil plane of the optical system, include the entrance pupil in these grids, and determine the positions of all grid points on the entrance pupil plane; for each grid point, determine the parameters of a traced incident ray, that is, the traced incident ray passes through the object point, and the incident direction of the traced incident ray is along the connection line between the object point and the grid point; traverse all grid points on the entrance pupil plane and determine the parameters of all traced incident rays in the same way; Step S2.3: Determine the paths that all traced incident rays travel from the object point to the virtual reference sphere; Step S2.4: Calculate the optical paths that all traced incident rays travel from the object point to the virtual reference sphere; Step 3: Calculate the optical path that the chief ray travels from the object point to the exit pupil plane; Step 4: Solve the wave aberration of the optical system using the optical paths obtained in Step 2 and Step 3.

2. A method for solving the wave aberration of an optical system by ray tracing according to claim 1, characterized in that, The wave aberration of the optical system is the optical path difference between the actual wavefront and the reference wavefront of the optical system. The reference wavefront is a spherical surface, and this spherical surface is defined as the virtual reference sphere. The center of the virtual reference sphere is located at the position of the Gaussian image point, and the radius of curvature of the virtual reference sphere is the distance between the center of the exit pupil and the Gaussian image point.

3. A method for solving the wave aberration of an optical system by ray tracing according to claim 2, characterized in that, The specific operation steps of Step 1 are as follows: Step S1.1: Using Gaussian optical imaging theory, according to the position of the object point and the composition of the optical system components, successively image the object point using each optical element in the optical system, and calculate the position of the Gaussian image point formed by the object point after passing through the optical system. This Gaussian image point is the center of the virtual reference sphere; Step S1.2: According to the position parameters of the aperture stop of the optical system and the composition of the optical system components, calculate the position of the exit pupil of the optical system, and calculate the distance between the center of the exit pupil and the Gaussian image point. This distance is equal to the radius of curvature of the virtual reference sphere.

4. A method for solving the wave aberration of an optical system by ray tracing according to claim 1, characterized in that In Step S2.2, the resolution of the grid is 64*64 or 128*128.

5. A method for solving the wave aberration of an optical system by ray tracing according to claim 1, characterized in that, The specific operation steps of Step S2.3 are as follows: Trace the propagation paths of each incident ray among all the traced incident rays. The propagation paths include the normal propagation path and the reverse extension line propagation path. If the virtual reference sphere is on the light propagation path, it is the normal propagation path. At this time, calculate the intersection point between the incident ray and the virtual reference sphere; If the virtual reference sphere is in the direction opposite to the light propagation direction, it is the reverse extension line propagation path. At this time, calculate the intersection point between the reverse extension line of the incident ray and the virtual reference sphere.

6. A method for solving the wave aberration of an optical system by ray tracing according to claim 5, characterized in that, The specific operation steps of Step S2.4 are as follows: For each incident ray among all the traced incident rays, first, according to its propagation path in the optical system, calculate the optical path it travels from the object point to the last optical element of the optical system, and then, based on the exit point and exit direction of the incident ray on the last optical element of the optical system, calculate the optical path the incident ray travels from the last optical element of the optical system to the virtual reference spherical surface.

7. A method for solving the wave aberration of an optical system by ray tracing according to claim 6, characterized in that, In step S2.4, use the two-dimensional matrix Ψ1 to represent the optical path that the light beam emitted from the object point travels from the object point to the virtual reference spherical surface: where a(x i , y j ) represents the optical path that the incident light ray with normalized coordinates (x i , y j ) travels from the object point to the virtual reference spherical surface, i = 1...m, j = 1...n, and the two-dimensional matrix Ψ1 has a size of m×n.

8. A method for solving the wave aberration of an optical system by ray tracing according to claim 7, characterized in that, The specific operation steps of step three are as follows: Assume that the optical path that the chief ray travels from the object point to the exit pupil surface is b, define a two-dimensional matrix Ψ2 of the same size as the two-dimensional matrix Ψ1, and all its elements are b. The two-dimensional matrix Ψ2 represents the optical path that the light beam emitted from the object point travels through the optical system to the actual wavefront. 。 9. A method for solving the wave aberration of an optical system by ray tracing according to claim 8, characterized in that, The specific operation steps of step four are as follows: Define a two-dimensional matrix Δ that describes the wave aberration data of the optical system. The size of the two-dimensional matrix Δ is m×n, and the calculation formula for the two-dimensional matrix Δ is formula (3) or formula (4). Δ = Ψ1 - Ψ2 (3) Δ = Ψ2 - Ψ1 (4).

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